24 Leonard Susskind and George Hrabovsky wrote a book that purports to set out the minimum amount of mathematics that one needs to know in order to do physics. The Theoretical Minimum (2013). The mathematics they include goes well beyond trigonometry and calculus.
25 The authors probably should have said “basic laws of mathematics that the Pythagorean School probably knew about.”
Economics and Other Social Sciences
I became interested in the matters discussed herein during my university study of economics. I encountered and investigated a variety of methodological issues concerning the construction and testing of theories, the use of mathematics (and statistics) and the relevance of empirical evidence. Much of the discussion that interested me, and that was clearly secondary to the mainstream work of economists, addressed the question of whether economics is a “science.” I discovered that in the mid-twentieth century, in the midst of controversy over certain aspects of neo-classical price theory, some leading economists had become engaged in a heated debate over methodology. The heart of the debate—what are we trying to accomplish with our theories and how do we judge or assess our degree of success—has application in a wide range of intellectual and policy activities.
Subsequently, I became intrigued by the obvious parallels (or overlaps) between this brief debate among economists and the substantial body of learning that existed in the philosophy of science. Clearly, the questions that the economists considered were relevant to, and similar to, experiences in certain branches of the natural sciences, particularly biology and physics. Of course, had I been a student of physics first and come to economics later, I might be expressing surprise that the methodological issues of physics have parallels in the field of economics; however, it seems to me that, independent of my experiences, there are potential benefits for the lay reader in confronting the methodological issues in the context of economics rather than biology or physics, because the concepts and subjects of economics generally feel more approachable for the non-scientist.
In this day and age, it will seem strange to many people for me even to include a discussion of economics in a book on the sciences. The last few years have dramatically altered the public perception of the profession. And, if the status of a discipline as a science is to be determined by the ability of the discipline to make concrete and accurate projections about the consequences of various actions, then economics in the early twenty-first century should strive to keep a low profile.
“Physics envy”
In September 2010, The New York Times labeled as the “Idea of the Day” the views of columnist Gideon Rachman of The Financial Times that: “Economists would do well to learn the modesty of historians….” September 9, 2010. Mr. Rachman warned about economists (pointing to Nobel Prize winner Joseph Stiglitz) who, in the face of recent failures, would “simply search for ‘new paradigms’—and then presumably go back into the business of scientific prediction.” He noted, “With the exception of a few deluded Marxists, historians know that their work cannot be used to predict the future. History can suggest lessons and parallels and provide wisdom—but what it cannot do is provide a sociological equivalent of the laws of physics. Yet this seems to be the aspiration of many economists, who notoriously suffer from ‘physics envy.’” FT.com, 6 September 2010.
The same theme appeared in an opinion column by political scientists Kevin A. Clarke and David M. Primo a year and a half later. “Overcoming ‘Physics Envy,’” The New York Times, April 1, 2012, p.9. They assert that social sciences are suffering from the efforts to use the hypothetico-deductive method that has been idealized as “the” method of the hard sciences (formulate a theory, deduce testable empirical hypotheses from the theory, then test the hypotheses—if the evidence contradicts the prediction, then the theory needs to be rejected or revised; if it is consistent with the hypothesis, then the theory is deemed tentatively confirmed, or, perhaps more accurately, not yet disconfirmed). They argue that this model does not accurately represent even how the hard sciences are practiced, ignoring “everything messy and chaotic” that inevitably accompanies scientific inquiry.
More importantly, they argue that empirical testing and even empirical predictions are not necessary for “good science,” noting that many useful theoretical models help explain and enable us better to understand phenomena, even though they do not give rise to testable predictions or even, sometimes, where they are obviously false. (They also assert that the analysis of empirical data can be helpful even in the absence of a grand theory.) “To borrow a metaphor from the philosopher of science Ronald Giere, theories are like maps: the test of a map lies not in arbitrarily checking random points but in whether people find it useful to get somewhere.” Id.
Interestingly, during the late nineteenth and early twentieth centuries, successes at incorporating mathematical methods of analysis into increasingly elaborate deductive theories, in models that bore striking similarities to classical mechanics, led economists increasingly to identify themselves as different from and superior to the other social sciences. Thus, in 1891, John Neville Keynes, the father of John Maynard Keynes (in turn, the father of “Keynesian economics”), quoted Alfred Marshall as saying: “It is vain to speak of the higher authority of a unified social science. No doubt if that existed, economics would gladly find shelter under its wing. But it does not exist; it shews no sign of coming into existence. There is no use waiting idly for it; we must do what we can do with our present resources.” The Scope and Method of Political Economy (1891), p.110.
Keynes himself observed: “Students of economics may, moreover, naturally and fairly ask to have the province of sociology itself more explicitly defined, and to see its own fundamental doctrines more clearly formulated, before they can be expected to show a willingness to have political economy subsumed under and absorbed into it.” Id., p.134.
History as science
Whatever may be said about the “humility” of the historian in our contemporary world, there are indications that at least some historians, as well as other social scientists, have aspirations to achieve the same status as the natural sciences.
For example, Jared Diamond and James A. Robinson (eds.) in Natural Experiments of History (2010) discuss history as a science.1 In their prologue, the editors complain that “laboratory scientists …look[ ] down on fields of science that cannot employ manipulative experiments” and observe that, nonetheless, “there are many fields widely admitted to be sciences” in which it is not possible to conduct experiments, citing evolutionary biology, paleontology, epidemiology, historical geology and astronomy. Id., p.1. They go on to discuss the use in history of “natural experiments” or comparative methods “preferably quantitative[ ] and aided by statistical analyses." Id., pp.1–2.2 The book then describes several such studies or experiments.
In this context, it is worth noting that some practitioners of these other sciences, such as evolutionary biology, have sought to emulate, as far as possible, the methodological approaches of physics in the use of laws and mathematical techniques. See, e.g., Martin A. Nowak (with Roger Highfield), Super Cooperators (Altruism, Evolution, and Why We Need Each other to Succeed) (2011), pp.1–2, et seq.
Two things are likely to strike the reader of Natural Experiments of History. First, it is surprising that the application of comparative analyses and statistical methods in historical studies would be viewed as innovative or controversial. One would have thought that the potential benefits of such techniques would have been obvious and that it was eminently sensible to see what results could be achieved. (“History is full of such potential experiments; it is just that historians have not yet thought of them in these terms.” Id., p.249.) Second, it is surprising that such highly respected and accomplished historians as the editors would take such an apologetic and defensive approach to the subject—the useful question is not how